Graphene obtained by mechanical exfoliation of graphite displays unique electronic properties with high mobility and saturation velocity. However, this is not a scalable technique, the film being limited to small area. Large area synthesis of good quality graphene has been achieved by CVD. The choice of substrate apparently influences the electronic properties of graphene. Most of reports have used SiO2-Si due to the widespread availability, but it is a poor choice of the material to degrade the graphene performace. In this thesis, more ideal platforms are introduced, including single crystal diamond (SCD), nanodiamond (ND), and diamond-like-carbon (DLC). It was found that different terminations for substrates caused strong effects for graphene properties. For H-terminated diamond, it was found that a p-type layer with good mobility and a small bang gap, whilst when N/F-terminations are introduced it was found that a layer with more metallic-like characters arises. Furthermore, different orientations of H-terminated SCD(100)/(111) were found to induce different band-gap of graphene. Simulation analysis proves the difference. However, the mobility results of graphene-H-terminated ND herostructure are better than graphene supported by SCD, which offers the prospect of low cost sp2 on sp3 technology. Raman and XPS results reveal the influence from the C-H band of ND surface. Impedance measurements show two conductive paths in the graphene-HND heterostructure. Graphene FET was built on this heterostructure, which exhibited n-type and high mobility. The family of amorphous carbon films, DLC, appeal to a preferable choice of graphene supporting substrate since IBM built the high-frequency graphene FET on DLC. For N-termination it was found that the optical band gap of DLC shrinked, whilst for F-terminated DLC it was found that fluorine groups reduce the DLC’s surface energy. Owing to different phonon energies and surface trap densities, graphene-DLC heterostructures give different electronic properties and offer the prospect for 2D lateral control applications.